Butt Cannon

"I've got machine guns... in my butt?!"

— Astro, Astro Boy

A ranged weapon integrated within the character's buttocks. Often used as a surprise attack.

Examples:

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Anime & Manga

Astro Boy is probably the trope maker, as pictured above with a pair of machine guns mounted in his rear.
In Keijo!!!!!!!!, Ikumi Yuzuki is the creator of the "Vacuum Butt Cannon" technique. In order to perform this technique, it requires a buildup of numerous, rapid and violent twists of the hip, and when fully charged, unleashes a powerful linear shockwave from the user's butt, capable of shredding the swimsuits of their opponents.
In Asobi Asobase, Maeda, Hanako's butler, gained the ability to fire lasers out of his butt when an alien device was inserted into his anus.

Films

The kung fu film Kid from Kwangtung has a lion dance-slash-fight scene in its opening where the protagonist wears a chicken suit to fight a bunch of rival challengers, whom are parading in a giant centipede suit. The hero's chicken suit contains a secret projectile launcher that fires yellow gunk in its butt, with the hero shouting, "Taste my chickenshit!" before shooting it at some opponents.

Literature

Like all dwarfs in the Artemis Fowl universe, burglar Mulch Diggums tunnels through the earth by ingesting soil, passing it through his digestive tract at high speed, then ejecting it out the... erm, other end. The excretion process is so forceful that Mulch weaponises it on occasion, generally once per book.

Live-Action TV

The Doom Patrol (2019) episode "Doom Patrol" has a man who can make an artillery cannon come out of his ass appear as an associate of the supervillain Codpiece.

Tabletop Games

BattleTech has rear-mounted weapons on some mechs, but most of the time they're located in the back or shoulder region of the mech. There are a few, however, that have weaponry mounted in something closer to the butt region, most notably the four-legged Balius◊ omnimech, which is stylized to look like a mechanical horse with lasers for its "tail."

Video Games

Mr. Toots, the unicorn gun from Red Faction. Mr. Toots shoots rainbow laser blasts out of his butt.
Featured in Astro Boy: Omega Factor as a Smart Bomb.
The first boss of Einhänder, Drache, first a Wave-Motion Gun out of its butt.
On a larger scale, Star Control II has the Spathi, a cowardly race whose ships come equipped with a rear-facing Backwards Utilizing Tracking Torpedo launcher. Their standard tactic is to run away while farting out missiles at the pursuing ship.

Web Original

The abridged Gag Dub of Sonic the Hedgehog: The Movie depicts the giant Eggman mecha as having one. Per Tails: "Is it a cannon in his butt, or is it a cannon that fires butts? (It's the first, as he soon discovered.)
Scanlan of Critical Role manages to aim and fire a Call Lightning spell from his backside, in an attempt to impress Pike. Sam Riegel, his player, lampshades this.
Sam: I have practice aiming things with my ass in this campaign!

Western Animation

Teenage Mutant Ninja Turtles (2012) introduces the Kraang Biotroids in Season Two. They are large, ape-like, bio-mechanical heavy infantry units with nipple saws and butt cannons, as seen 20 seconds into this preview.
The Grim Adventures of Billy & Mandy: In the episode "It's Hokey Mon!" one of the many eponymous Hokey Monsters has a literal cannon in its butt, which another Hokey Monster loads cannonballs in manually.
Evil Con Carne: In the Pilot Episode, Hector gets a new robot body with all sorts of functions, such as butt rocket launchers. When he uses them, however, he destroys most of his base and puts himself in mortal peril.
Futurama: In the episode the gang goes back to Revolutionary times, someone tries to use Bender as a cannon. Much to Bender's surprise, it works (with the ball coming out his butt).
An episode of Danny Phantom where a ghost erases Danny's memories, how to use his powers included, has him attempt to use his ghost ray by firing it from his hands. Instead, however, he somehow accidentally channels it through his rear. Naturally, Danny lampshades the ridiculousness of it.
Danny: That can't be right, but it'll have to do!
In Spongebob Squarepants in the episode "Spy Buddies" Patrick is given a special pair of pants that have this ability. They're used for SpongeBob and him to break into the Chum Bucket.
In Steven Universe the Show Within a Show "Dogcopter" features a robotic helicopter dog that can shoot missiles out of his butt.

Real Life

The Bombardier Beetle's first line of defence against threats is to turn round, elevate its rear end, point its cloaca at its assailant and fire an almost boiling hot stream of noxious chemicals with a loud popping noise. Hence the name.
One of the most infamous examples of this trope is the skunk, which have glands in their rear capable of spraying a horrific smelling musk. They can spray a good distance with surprising accuracy.